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To play Words with Friends/Scrabble optimally, you need to think about how your current plays affect future plays. As we've already seen, this means it is best to think about the future and work backward from there. Essentially, game situations are candidates for backward induction. In this video, I use this technique to explain why you should not try to maximize your own score exclusively.

You can find more of these strategies in a couple of books I wrote. The emphasis is on teaching the underlying mechanics of Words with Friends than rote memorization; I drew heavily from game theoretical concepts as I wrote the books. The first is the short version; the second is the longer version.